\(\dfrac{5}{2x+1}=\dfrac{1}{x-4}\)

\(\Leftrightarrow\dfrac{5\left(x-4\right)}{\left(2x+1\right)\left(x-4\right)}=\dfrac{1\left(2x+1\right)}{\left(x-4\right)\left(2x+1\right)}\)

\(\Leftrightarrow5\left(x-4\right)=1\left(2x+1\right)\)

\(\Leftrightarrow5x-20=2x+1\)

\(\Leftrightarrow3x-21=0\)

\(\Leftrightarrow3x=21\)

\(\Leftrightarrow x=7\)